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9.2.2 A Simple Problem with Mixed Attributes
The problem that we are going to solve here consists again in deciding whether
or not to play tennis, with the difference that now we are going to use the
dataset of Table 9.3 to train our decision trees. So, the attribute set will con-
sist again of A = {O, T, H, W} and the set of terminals of T = {a, b}, with the
difference that now the attributes TEMPERATURE and HUMIDITY will
both branch off into two (“less than or equal to” and “greater than”). Further-
more, a set of 10 integer random constants ranging over the interval [60, 99]
and represented by the numerals 0-9 will be used, giving R = {0, ..., 9}. As
usual for this kind of illustrative problem, a small population size of 20 indi-
viduals evolving for just 50 generations will be used so that we can scruti-
nize a successful run in its entirety. The complete list of parameters used in
this experiment is shown in Table 9.4.
The evolutionary dynamics of the successful run we are going to analyze
here is shown in Figure 9.10. And as you can see, in this run, a perfect solu-
tion was found in generation 6.
14
Best Ind
Avg Fitness
12
10
8
6
4
2
0
0
5
10
15
20
25
30
35
40
45
50
Generations
Figure 9.10.
Progression of average and best fitnesses obtained in the illustrative
run of the play tennis problem with mixed attributes.
The initial population of this run, together with the fitness of each individual
evaluated against the training set of Table 9.3, is shown below. As you can
see, we were lucky this time, and the best two individuals of this generation
have both fitness 10 (these individuals are shown in bold):
